Abstract
Modern credit risk measurement and management systems depend to a great extend on three key risk parameters: probability of default (PD), exposure at default (EAD), and loss given default (LGD). PD describes the probability that the lending institution will face the default of some obligor or transaction. EAD gives an estimate of the exposure outstanding at the time of the default, also indicating the maximum loss on the respective credit products. Finally, LGD measures the credit loss a bank is likely to incur due to an obligor default.
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Notes
- 1.
This article will use the expressions credit product and (credit) facility interchangeably as generic terms for all credit risk bearing instruments of a bank.
- 2.
International Accounting Standard/International Financial Reporting Standard.
- 3.
See for example Altman et al. (2005) or the articles available at http://www.defaultrisk.com
- 4.
See BCBS (2004) for the full text as well as additional rules not mentioned here (for example, concerning documentation, stress tests, overrides, etc.). The reader should also take the respective regulations of national supervisors into account.
- 5.
For purchased receivables, see §§ 364 and 367.
- 6.
NPL is used as an abbreviation for non-performing loan.
- 7.
See IAS 39.8, IASB (2005), for a definition of fair value.
- 8.
As an alternative to cash flow adjustment, one may apply a discount rate adjustment approach. In this case, one may refer under certain circumstances to similar risk-adjusted discount rates as used for LGD estimation; see Sect. 9.6.2.4.
- 9.
Some of the necessary modifications are addressed below.
- 10.
Due to restricted data availability, differences might be greater in theory than in banking practice.
- 11.
This will be necessary if a bank defines its PD ratings as local currency ratings.
- 12.
Note that differences in default definition will therefore affect economic loss.
- 13.
As an alternative, one might define V(t, p) as the net present value of all future recoveries and costs of the facility in case of no default in t. While theoretically appealing, such a definition can be difficult to implement in practice. Furthermore, it would also require a respective definition of EAD as might be done in internal models only.
- 14.
See, for instance, Chaps. 10 and 11 for more details on EAD estimation.
- 15.
Exemptions may be possible if such extraordinary recoveries are observed on a regular basis.
- 16.
Incongruence can lead to losses or gains depending on the level of interest rates at the time of credit granting and default. It is therefore sometimes argued that gains will offset losses due to the mean reversion property of the interest rate.
- 17.
If available, one may also consider market values of loans or credit derivate instruments.
- 18.
See CEBS (2005), § 234.
- 19.
I.e. δ sc (SC)  = 1 for SC = sc and δ sc (SC) = 0 otherwise.
- 20.
To simplify the presentation, time references are left out in (9.3) as well as in most of the formulas following. It is generally assumed in this article that one intends to predict the loss quota for a default occurring within a time interval T = [t a , t e ) given the information up to t 0 (the time where the computation takes place), i.e. LGD j = LGD j (T|t 0).
- 21.
This article uses the expression “risk mitigation instrument“ (rmi) as a general notion for all kind of collateral and guarantees.
- 22.
However, as mentioned above one should include references into the loss file in order to allow for a later replacement of non-cash recoveries by the corresponding cash recoveries realized from the respective cured or restructured facilities. Note that non-cash recoveries are generally estimates of future, uncertain cash flows.
- 23.
For example, repossession and sale of collateral might already be finished for a defaulted credit product. The respective information can then be used to update the estimate of the recovery rate for the respective collateral type(s) while at the same time the information required to re-estimate the recovery rate for unsecured exposure might still be incomplete.
- 24.
An example of how this information may be used in LGD estimation is given in Sect. 9.6.2.3.
- 25.
While being simple from a pure statistical point of view, setting up a procedure that generates reasonable LGD predictions based on different types of information will nevertheless often remain a demanding task.
- 26.
A comprehensive survey of empirical analyses can be found in Bennett et al. (2005); the following mentions only a few of them.
- 27.
Altman and Kishore (1996) and Acharya et al. (2004) found significant differences in recoveries of defaulted bonds belonging to different seniority classes. The same authors report significant differences for only some industry sectors, while Araten et al. (2004) could not find significant impact of industry (or region) on LGDs observed for loans.
- 28.
- 29.
- 30.
See for example Franks et al. (2004) for an analysis of recovery processes and rates in the U.K., France, and Germany. Useful information about doing business in different countries may also be found at http://www.doingbusiness.org.
- 31.
- 32.
A loss case will generally comprise all credit products of a defaulted entity.
- 33.
Details of this approach are considered in the next section for collateral recoveries.
- 34.
The same holds true for other components of LGD, see for example Sect. 9.6.2.3.
- 35.
In order to estimate PD, EAD, and LGD in a consistent way, one will often apply a cohort approach for all three variables. Therefore the last valuation before default is the more appropriate reference value.
- 36.
This may sometimes be the case during the introduction of Basel II compliant processes.
- 37.
For unsecured exposures, recovery estimates may be derived from market LGDs; see Sect. 9.4.
- 38.
The following considers guarantees to simplify the presentation. Credit derivatives can often be treated in a similar way.
- 39.
Again, j indicates the facility and l the exposure part secured by the guarantee.
- 40.
In practice, the value of a guarantee may depend on further warranty clauses. To mention a few, guarantees may cover only a subset of the borrower’s obligations, for example only interest rate payments or redemption. They may also be restricted to protect certain risk classes only (for example, no political risks). Furthermore, they may (partly) protect residual loss after recovery of other collateral and the bankrupt’s assets only. This article does not consider the modifications necessary to adequately value such guarantees. Note that some characteristics mentioned above may also be incompatible with Basel II requirements for eligible guarantees and can therefore only be considered in internal models.
- 41.
See BCBS (2004), §§ 284 (i)–(iii) and 307 (i), (ii).
- 42.
In fact, a bank may use both techniques simultaneously for different purposes. For example, explicit simulation of guarantees may sometimes be too time-consuming so that LGD numbers already including the risk mitigation effect have to be applied instead.
- 43.
It may sometimes be possible to detect certain types of dependences automatically. For example, knowledge on economic interdependence of different addresses, which might be available in the institute’s IT-systems (for example, in form of borrower units), can be used to decide whether (or to what extent) a guarantee is eligible for a facility of a certain borrower.
- 44.
The potential for optimization stems from the joint effect of different risk mitigation instruments, possible currency mismatches, changes in exposure class due to risk mitigation, etc.
- 45.
Information on external costs will generally be collected in the CLDB. This assures its availability.
- 46.
Since IAS requires the application of the effective original loan rate, a bank may think about applying this rate in its estimates if LGD numbers are used for IAS purposes as well.
- 47.
Means of fulfilling this requirement were discussed in Sect. 9.6.2.2.
- 48.
Volatility of LGD then has to be recognized separately in unexpected loss estimates.
- 49.
For example, she may elect the respective after-default scenario or modify the time structure of future recovery cash flows.
- 50.
(N)PL-LGD is used as an abbreviation for an LGD of a (non)performing exposure.
- 51.
One may also think about allowing analysts to judge the uncertainty of recoveries as well, giving them the possibility to influence stress factors, etc. Any degree of freedom in the applied procedure, however, may not only improve the quality of estimates but also bears the danger of deterioration and generally also complicates the whole procedure – from implementation and workflow aspects up to a later validation.
- 52.
Cf. Chaps. 14 and 15.
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Peter, C. (2011). Estimating Loss Given Default: Experience from Banking Practice. In: Engelmann, B., Rauhmeier, R. (eds) The Basel II Risk Parameters. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16114-8_9
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